© boardworks ltd 2006 1 of 27 a6 real-life graphs ks3 mathematics

© Boardworks Ltd 2006 1 of 27

A6 Real-life graphs

KS3 Mathematics


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AA6.1 Reading graphs

Contents

A6 Real-life graphs

A6.2 Plotting graphs

A6.3 Conversion graphs

A6.5 Interpreting graphs

A6.4 Distance-time graphs


Graph of monthly mobile phone charges


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Contents

A6 Real-life graphs

A6.1 Reading graphs





Plotting graphs – using a table of values

When we plot a graph we usually start with a table of values.

The values in the table usually come from a formula or equation or from an observation or experiment.

For example, a car hire company charges £30 to hire a car and then £25 for each day that the car is hired.

This would give us the following table of values:

The cost of the car hire depends on the number of days. The number of days must therefore go in the top row.

Number of days, d

Cost in £, c

1 2 3 4 5

55 80 105 130 155


Plotting graphs – choosing a scale

The next step is to choose a suitable scale for the axes.

Look at the values that we need to plot.

Number of days, d

Cost in £, c

1 2 3 4 5

55 80 105 130 155

The number of days will go along the horizontal axis.

The numbers range from 1 to 5.

A suitable scale would be 2 units for each day.

The cost will go along the vertical axis.

The cost ranges from 55 to 155.

A suitable scale would be 1 unit for each £10. We could start the scale at £30.


Plotting graphs – drawing the axes

We then have to draw the axes using our chosen scale.

We will need at least 10 squares for the horizontal axis and 13 squares for the vertical axis.

When the scale does not start at 0 we must show this with a zigzag at the start of the axis.

Number the axes.

30405060708090

100110120130140150

0 1 2 3 4 5

Label the axes, remembering to include units, if necessary.

Number of days

Cos

t (£

)


Plotting graphs – plotting the points

Use the table of values to plot the points on the graph.

Number of days, d

Cost in £, c

1 2 3 4 5

55 80 105 130 155

00

30405060708090

100110120130140150

1 2 3 4 5

Number of days

Cos

t (£

)

It is most accurate to use a small cross for each point.

If appropriate, join the points together using a ruler.

Lastly, don’t forget to give the graph a title.

Cost of car hire


Science experiment

Mass of object moving down ramp (grams)

Time taken for object to move down ramp (seconds)

100

4

150

7

200

12

250

17

A group of pupils are doing an experiment to explore the effect of friction on an object moving down a ramp.

They attach weights of different mass to the object and time how long the object takes to reach the bottom of the ramp.

They put their results in a table and use the table to plot a graph of their results.


Science experiment

Mass of object moving down ramp (grams)

Time taken for object to move down ramp (seconds)

100

4

150

7

200

12

250

17

Mass of object (grams)

0

4

8

12

16

20

0 50 100 150 200 250 300

Tim

e ta

ken

(se

con

ds)

We can join the points using straight lines.

Do the intermediate points have any practical significance?

How could we make the graph more accurate?


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Contents

A6 Real-life graphs


A6.1 Reading graphs




Plotting a conversion graph

Let’s plot a graph to convert pounds to euros.

First we need a table of values:

€

£ 200

300

20 100 160

30 150 240

This gives us the points:

(20, 30)

(100, 150)

(160, 240)

(200, 300)

0 50 100 150 2000

50

100

150

200

250

300

£

€

A conversion graph for pounds to euros


Conversion graphs – money


Conversion graphs – temperature


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Contents

A6 Real-life graphs


A6.1 Reading graphs




Distance-time graphs

In a distance-time graph the horizontal axis shows time and the vertical axis shows distance.

The below distance-time graph shows a journey.

What does the slope of the line tell us?

The slope of the line tells us the average speed.

The steeper the line is, the faster the speed.

0 time

dist

ance


Label the distance-time graph


Olympic swimmers


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Contents

A6 Real-life graphs


A6.1 Reading graphs




Filling flasks 1


Filling flasks 2


Interpreting the shapes of graphs

150

0

50

100

10 20 30 40 50 60 700 80 90 100

Eating a bar of chocolate

Ma

ss o

f ch

oco

late

(g

)

Time (seconds)

Jessica eats a bar of chocolate. This graph shows how the mass of the chocolate bar changes as it is eaten.


Interpreting the shapes of graphs

This graphs shows how the temperature of the water in a pan changes when frozen peas are added.

Time

Te

mp

era

ture

of w

ate

r


Which graph is correct?

In an experiment a group of pupils poured water onto a sponge and weighed it at regular intervals.

Each time the sponge soaked up all the water.

Which graph is most likely to show their results?

Mas

s of

spo

nge

(g)

Volume of water (cm3)

Mas

s of

spo

nge

(g)


Mas

s of

spo

nge

(g)


Graph A Graph B Graph C Graph D

Mas

s of

spo

nge

(g)



Sketching graphs

A group of pupils are conducting an experiment. They fill three beakers with boiling water and record the temperature of the water over time.

Beaker A has no wrapping, Beaker B is wrapped in ice and Beaker C is wrapped in insulation fibre.

The temperature graph for beaker A looks as follows:

Time (minutes)

Tem

pera

ture

(o C

)

Beaker A

How would the graphs for beakers B and C compare to this?


Sketching graphs


Matching graphs to statements

© boardworks ltd 2006 1 of 27 a6 real-life graphs ks3 mathematics

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